The weight of the load carried by a small cargo truck is 2050 pounds with a vari

Question

The weight of the load carried by a small cargo truck is 2050 pounds with a variance of 12100 pounds ^ 2. It is known that the total load follows a Normal distribution.

A truck receives a fine if it weighs more than 2250 pounds. What is the probability that a truck will receive a fine?

b. What weight should a truck carry to be in the 80 percent percentile?

c. What is the probability that the actual truck weight is between 2000 and 2200 pounds?

d. If a scale is used that records the weight with an accuracy of 5 pounds (bone rounds to the nearest five pounds), what is the probability that the weight recorded is between 1995 and 2005 pounds inclusive?

e. What is the probability that the actual weight of a truck is 2100 pounds?

f. A sample of 25 trucks is taken, what is the probability that the average of the sample is between 2000 and 2100 pounds?

Explanation / Answer

Ans:

Given that

mean=2050

variance=12100

standard deviation=sqrt(12100)=110

a)

z=(2250-2050)/110=1.818

P(z>1.818)=0.0345

b)P(Z<=z)=0.8

z=0.8416

x=2050+0.8416*110=2142.58

c)

z(2000)=(2000-2050)/110=-0.45

z(2200)=(2200-2050)/110=1.36

P(-0.45<z<1.36)=P(z<1.36)-P(z<-0.45)=0.9137-0.3247=0.5890

e)P(x=2100)=NORMDIST(2100,2050,110,FALSE)=0.0033

f)standard error of mean=110/sqrt(25)=22

z(2000)=(2000-2050)/22=-2.27

z(2100)=(2100-2050)/22=2.27

P(-2.27<=z<=2.27)=P(z<=2.27)-P(z<=-2.27)=0.9885-0.0115=0.9770

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